Capacitors, which store electric charge, are one of the basic building blocks of electronic circuits. In its most basic form, a capacitor comprises two conductive surfaces separated from one another by a small distance, wherein a nonconductive dielectric material lies between the conductive surfaces. The capacitance C of such an arrangement is proportional to KA/d, wherein K is the dielectric constant of the middle material, A is the area of the opposing conducting surfaces, and d is the distance between the conducting surfaces.
FIG. 1 is a side cut-away isometric view of a multilayer capacitor 120. The capacitor 120 has two external connections or electrodes 124 and 128, shown on the left and right, respectively. Connected to the electrode 124 are a number of generally parallel conductive sheets or plates 130. Likewise, connected to the electrode 128 are a number of generally parallel conductive sheets or plates 140. The conductive plates 130 and 140 intermesh as shown. Between the conductive plates 130 and 140 is a dielectric material 150. An optional casing 160 can be used to cover the external faces of the capacitor 120 between the electrodes 124 and 128. The multilayer arrangement results in a multiplicative increase in capacitance proportional to the number of intermeshed plates. In fact, the formula for the capacitance of this arrangement is proportional to nKA/d where n is the number of plates from each electrode.
When the dielectric material 150 is a ceramic, the capacitor 120 is a multilayer ceramic capacitor (MLCC). MLCCs have become popular because ceramic materials are available with a desirably high dielectric constant. Ceramic dielectric materials can also be fabricated in thin layers, resulting in a small interplate spacing d, and thereby increased capacitance. A ceramic dielectric material is typically formed by mixing a ceramic powder with an organic binder, which acts like a slurry. When the ceramic hardens, it holds the electric plates 130 and 140 in place.
FIG. 2A is a schematic diagram of an equivalent circuit model 200 of a capacitor, such as the multilayer capacitor 120. In the model 200, the terminals 210 and 220 represent the electrodes 124 and 128. The equivalent circuit model 200 comprises a capacitance C, a parallel resistance RP, a series resistance RS, and an inductance L. In an ideal capacitor, only the capacitance C would be present. The parallel resistance RP, series resistance RS, and the inductance L arise from unwanted or nonideal effects in a real capacitor. For example, if there is some leakage current flowing through the dielectric material 150, that is modeled by the parallel resistance RP. As another example, if there is some resistance in the electrodes 124 or 128, that is modeled by the series resistance RS. The combined effects of all resistances in a capacitor are jointly modeled as an equivalent series resistance (ESR), as shown in FIG. 2B, which is a simplified equivalent circuit model 250 of a capacitor.
There are many parameters that characterize a capacitor. Chief among them is, of course, capacitance C. Other parameters include ESR and the values of the other elements in the equivalent circuit model 200. Other capacitor parameters that usefully specify its behavior in alternating current (AC) circuits include loss angle, phase angle, power factor, and dissipation factor, all of which are measures of the loss in a capacitor when an AC signal is applied to its electrodes. They are related mathematically as follows:PF=cos(Φ)=sin(δ)DF=tan(δ)Φ+δ=π/2where PF is the power factor, DF is the dissipation factor, Φ is the phase angle, and δ is the loss angle in phasor notation. Dissipation factor can also be expressed in terms of ESR at a given AC frequency as follows:DF=ESR/Xcwhere Xc is the reactance of the capacitor at the given frequency.
Capacitor manufacturers typically specify their capacitors in terms of parameters such as capacitance C and dissipation factor DF. Manufacturers typically test their capacitors to ensure that they fall within acceptable limits before they are released for sale. If a capacitor, for example, has an excessively large dissipation factor it is rejected.
Manufacturers typically utilize testing machines to perform industry-standard tests to measure specified capacitor parameters. Such machines can automatically handle capacitors; subject them to specified electrical, mechanical, and/or environmental conditions; measure parameters; make a pass/reject decision on each piece based on the measurement results, and sort the tested capacitors based on the pass/reject decision. Examples of such machines are the model 3300 family of MLCC test stations made by Electro Scientific Industries, Inc. of Portland, Oregon. U.S. Pat. No. 5,842,579, which is incorporated by reference herein, describes one such machine.
A challenge faced by capacitor testing equipment is the challenge to make each measurement reliably, without introducing errors because erroneous pass/reject decisions either decrease yield rates, decrease testing throughput as rejected components are retested, or both.